Prime Minister John Key is due to announce 72 new knights and dames in two weeks' time after restoring the titles scrapped by the Labour government in 2000.
Just 13 of the 85 eligible have decided to remain as principal companions or distinguished companions of the New Zealand Order of Merit, The Weekend Herald understands.
Ihimaera told the newspaper it was not a matter of accepting or declining.
He said he simply did not want to become a "Sir".
"When I accepted the award, I accepted it on the basis that it was a New Zealand award."
A source close to Neill said he also had decided not become a "Sir".
The source said the actor felt it was a "backward move".
Neill could not be reached for comment yesterday.
All those eligible to switch titles have made their decision.
However, they have been told not to reveal it ahead of an official announcement on August 1 - after the 72 names have been sent to the Queen for approval.
But some have already made their choice clear.
All Black legend Colin Meads said he decided to accept after discussion with family, friends and other dignitaries.
"It just seemed the right thing to do."
Other New Zealanders who have decided to accept a title include barrister Deirdre Milne, political scientist Prof Margaret Clark, winemaker George Fistonich and lawyer David Gascoigne.
The Weekend Herald understands Maori academic Dr Ranginui Walker and former Speaker of Parliament Margaret Wilson have decided to keep their awards as they are.
Author Patricia Grace also declined, saying restoring titles was "a step backward".
Vincent O'Sullivan, emeritus professor of English at Victoria University, Wellington, said he chose not to accept a title because it didn't fit New Zealand "historically and socially".
